SOLUTION: Can you please help me graph this equation? y=-x^2+6x+5

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Question 128757: Can you please help me graph this equation?
y=-x^2+6x+5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph f%28x%29=-1x%5E2%2B6x%2B5, we need to plot some points. To do that, we need to plug in some x values to get some y values


So let's find the first point:



f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%28-2%29=-1%28-2%29%5E2%2B6%28-2%29%2B5 Plug in x=-2


f%28-2%29=-1%2A4%2B6%2A-2%2B5 Raise -2 to the 2nd power to get 4


f%28-2%29=-4%2B6%2A-2%2B5 Multiply -1 and 4 to get -4


f%28-2%29=-4%2B-12%2B5 Multiply 6 and -2 to get -12


f%28-2%29=-16%2B5 Add -4 and -12 to get -16


f%28-2%29=-11 Add -16 and 5 to get -11


So when x=-2, we have y=-11


So our 1st point is (-2,-11)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%28-1%29=-1%28-1%29%5E2%2B6%28-1%29%2B5 Plug in x=-1


f%28-1%29=-1%2A1%2B6%2A-1%2B5 Raise -1 to the 2nd power to get 1


f%28-1%29=-1%2B6%2A-1%2B5 Multiply -1 and 1 to get -1


f%28-1%29=-1%2B-6%2B5 Multiply 6 and -1 to get -6


f%28-1%29=-7%2B5 Add -1 and -6 to get -7


f%28-1%29=-2 Add -7 and 5 to get -2


So when x=-1, we have y=-2


So our 2nd point is (-1,-2)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%280%29=-1%280%29%5E2%2B6%280%29%2B5 Plug in x=0


f%280%29=-1%2A0%2B6%2A0%2B5 Raise 0 to the 2nd power to get 0


f%280%29=0%2B6%2A0%2B5 Multiply -1 and 0 to get 0


f%280%29=0%2B0%2B5 Multiply 6 and 0 to get 0


f%280%29=0%2B5 Add 0 and 0 to get 0


f%280%29=5 Add 0 and 5 to get 5


So when x=0, we have y=5


So our 3rd point is (0,5)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%281%29=-1%281%29%5E2%2B6%281%29%2B5 Plug in x=1


f%281%29=-1%2A1%2B6%2A1%2B5 Raise 1 to the 2nd power to get 1


f%281%29=-1%2B6%2A1%2B5 Multiply -1 and 1 to get -1


f%281%29=-1%2B6%2B5 Multiply 6 and 1 to get 6


f%281%29=5%2B5 Add -1 and 6 to get 5


f%281%29=10 Add 5 and 5 to get 10


So when x=1, we have y=10


So our 4th point is (1,10)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%282%29=-1%282%29%5E2%2B6%282%29%2B5 Plug in x=2


f%282%29=-1%2A4%2B6%2A2%2B5 Raise 2 to the 2nd power to get 4


f%282%29=-4%2B6%2A2%2B5 Multiply -1 and 4 to get -4


f%282%29=-4%2B12%2B5 Multiply 6 and 2 to get 12


f%282%29=8%2B5 Add -4 and 12 to get 8


f%282%29=13 Add 8 and 5 to get 13


So when x=2, we have y=13


So our 5th point is (2,13)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%283%29=-1%283%29%5E2%2B6%283%29%2B5 Plug in x=3


f%283%29=-1%2A9%2B6%2A3%2B5 Raise 3 to the 2nd power to get 9


f%283%29=-9%2B6%2A3%2B5 Multiply -1 and 9 to get -9


f%283%29=-9%2B18%2B5 Multiply 6 and 3 to get 18


f%283%29=9%2B5 Add -9 and 18 to get 9


f%283%29=14 Add 9 and 5 to get 14


So when x=3, we have y=14


So our 6th point is (3,14)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%284%29=-1%284%29%5E2%2B6%284%29%2B5 Plug in x=4


f%284%29=-1%2A16%2B6%2A4%2B5 Raise 4 to the 2nd power to get 16


f%284%29=-16%2B6%2A4%2B5 Multiply -1 and 16 to get -16


f%284%29=-16%2B24%2B5 Multiply 6 and 4 to get 24


f%284%29=8%2B5 Add -16 and 24 to get 8


f%284%29=13 Add 8 and 5 to get 13


So when x=4, we have y=13


So our 7th point is (4,13)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%285%29=-1%285%29%5E2%2B6%285%29%2B5 Plug in x=5


f%285%29=-1%2A25%2B6%2A5%2B5 Raise 5 to the 2nd power to get 25


f%285%29=-25%2B6%2A5%2B5 Multiply -1 and 25 to get -25


f%285%29=-25%2B30%2B5 Multiply 6 and 5 to get 30


f%285%29=5%2B5 Add -25 and 30 to get 5


f%285%29=10 Add 5 and 5 to get 10


So when x=5, we have y=10


So our 8th point is (5,10)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%286%29=-1%286%29%5E2%2B6%286%29%2B5 Plug in x=6


f%286%29=-1%2A36%2B6%2A6%2B5 Raise 6 to the 2nd power to get 36


f%286%29=-36%2B6%2A6%2B5 Multiply -1 and 36 to get -36


f%286%29=-36%2B36%2B5 Multiply 6 and 6 to get 36


f%286%29=0%2B5 Add -36 and 36 to get 0


f%286%29=5 Add 0 and 5 to get 5


So when x=6, we have y=5


So our 9th point is (6,5)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%287%29=-1%287%29%5E2%2B6%287%29%2B5 Plug in x=7


f%287%29=-1%2A49%2B6%2A7%2B5 Raise 7 to the 2nd power to get 49


f%287%29=-49%2B6%2A7%2B5 Multiply -1 and 49 to get -49


f%287%29=-49%2B42%2B5 Multiply 6 and 7 to get 42


f%287%29=-7%2B5 Add -49 and 42 to get -7


f%287%29=-2 Add -7 and 5 to get -2


So when x=7, we have y=-2


So our 10th point is (7,-2)


-------------- Let's find another point --------------


f%28x%29=-1x%5E2%2B6x%2B5 Start with the given function


f%288%29=-1%288%29%5E2%2B6%288%29%2B5 Plug in x=8


f%288%29=-1%2A64%2B6%2A8%2B5 Raise 8 to the 2nd power to get 64


f%288%29=-64%2B6%2A8%2B5 Multiply -1 and 64 to get -64


f%288%29=-64%2B48%2B5 Multiply 6 and 8 to get 48


f%288%29=-16%2B5 Add -64 and 48 to get -16


f%288%29=-11 Add -16 and 5 to get -11


So when x=8, we have y=-11


So our 11th point is (8,-11)


Now lets make a table of the values we have calculated 



 xy



 -2-11
 

 -1-2
 

 05
 

 110
 

 213
 

 314
 

 413
 

 510
 

 65
 

 7-2
 

 8-11
Now plot the points



Now connect the points to graph y=-1x%5E2%2B6x%2B5 (note: the more points you plot, the easier it is to draw the graph)